Much effort has been devoted to modeling hearing, for applications such as automatic speech recognition, noise cancellation, hearing aids, and music. A popular approach is to model the cochlea, a coiled snail-shaped structure that is part of the inner ear as shown in FIG. 1. The cochlea is a spiraling, fluid-filled tunnel embedded in the temporal bone, and converts acoustic signals into electrical signals transmitted to the brain. Sound pressure waves strike the eardrum, causing it to move inward and moving the three small bones of the middle ear, which are the hammer, anvil, and stirrup. The movement of the bones initiates pressure waves in the cochlear fluid. These pressure waves propagate along the cochlear partition, which, as shown in FIG. 2, consists of the basilar membrane BM, tectorial membrane TM, and organ of Corti OC. The organ of Corti OC is a collection of cells, including the sensory hair cells, that sit on the basilar membrane BM. The bases (bottoms) of these hair cells are connected to nerve fibers NF from the auditory nerve AN, and the apexes (tops) of the hair cells have hair bundles HB. There are two types of hair cells in the cochlea: inner hair cells IHC and outer hair cells OHC.
The human cochlea is believed to contain approximately 4,000 inner hair cells IHC and 12,000 outer hair cells OHC, with four cells radially abreast and spaced every 10 microns along the length of the basilar membrane BM. The tectorial membrane TM lies on top of the surface of the organ of Corti OC. A thin fluid space of about 4 to 6 microns lies between these two surfaces, which shear as the basilar membrane BM moves up and down. The hair cells are primarily transducers that convert displacement of the hair bundle HB (due to shearing between the tectorial membrane TM and the surface of the organ of Corti) into a change in the receptor current flowing through the cell, which is transmitted to the auditory nerve AN and processed by the brain.
Each point on the basilar membrane BM is tuned to a different frequency, with a spatial gradient of about 0.2 octaves/mm for a human, and about 0.32 octaves/mm for a cat. Roughly speaking, the cochlea acts like a bank of filters. The filtering allows the separation of various frequency components of the signal with a good signal-to-noise ratio. The range of audible frequencies is about 20 Hz to 16 kHz in the human cochlea and about 100 Hz to 40 kHz in the cat cochlea.
Modeling the function of the cochlea has been an active area of research for many years. For example, U.S. Pat. No. 4,771,196, titled “Electronically variable active analog delay line” and issued to Mead and Lyon on Sep. 13, 1988, describes an analog filter bank cascade for signal processing. This patent, the disclosure of which is hereby incorporated by reference, illustrates an electronically variable active analog delay line that incorporates cascaded differential transconductance amplifiers with integrating capacitors and negative feedback from the output to the input of each noninverting amplifier. “Lyon's Cochlear Model”, written in 1988 by Malcolm Slaney as Apple Technical Report #13, describes a digital filter bank cascade developed by Lyon as a model of the cochlea. Further details of the Lyon model may be seen by reference to the technical report, the disclosure of which is hereby incorporated by reference.
This model uses a cascade of second-order filters, each of which requires a number of computations every time the signal is sampled. Each filter has a set of coefficients associated with it, and must also store some previous computations. If the sampling rate is increased, or the number of filters is increased in order to increase resolution, the number of computations rises proportionally. Thus, the desire for better resolution and sampling of the acoustic signal is balanced against the computations required and the storage needed for each filter. A more efficient approach, such as the approach of the present invention, would reduce the computation required for the cascade and allow for a higher quality representation of the signal.
This problem is not limited to digitized signals represented by discrete amplitude levels, nor is it limited to acoustic signals. Rather, it applies to any sampled signal (represented by discrete time values). Although the disclosure herein describes the problem and the invention in the context of audio signal processing, one skilled in the art will recognize that the invention may be applied to any signal processing using sampling, including electrical waveform sampling and video signal processing.